Ok, I'll give you the rundown of my education so far:
Prior to last semester, I had a 3.74 GPA. Last semester I made a C in my first computer science class and shot my GPA down to a 3.48. I suppose I can always retake this class and get it back up there.
I'm currently at CC, and my state's CCs have a program that, if you complete the associate of science degree, it will transfer seamlessly as a junior to virtually all public (and some private) universities in the state.
Recently, the head of the computer science department at a university in my state visited our computer science class and spoke about his school and their program. The school itself is not particularly renowned (though it's a perfectly good school), but their school of computer science is very highly renowned. They offer the only undergraduate degree in bioinformatics (the field I'm interested in) in the state. They award full scholarships to students who complete the transfer degree program with a qualifying GPA. Mine is sufficient. I only have 8 more courses counting the ones I'm taking this semester to graduate with my associates degree. Then I'll be transferring.
My dream school is Vanderbilt. This is the school I'm aiming for for grad school. The head of the computer science department of the university mentioned above has two phds from Vanderbilt. He personally tries to help high achieving students get there, and I believe that if I make it clear to the department heads what my goals are, and do very well, they will help me to achieve it.
Of course the damning dark spot on my record will be the horrendous experience I had on my first college attempt back when I first started college. I flunked nearly everything, taking some classes several times and never passing them. I made no progress and it was just a complete failure of unbelievable proportions. I took a four-year gap and started at my current college. Since then my grades have been good.
So, what do you think? Go for it, or give up the dream?
I would say go for it, persistence is key, and failure is just part of the process. No one succeeds without failing and if you're not failing then you're not trying.
Past may be a dark spot, but graduate admissions are more than just a look at your transcripts -- there are essays where you can make your case, and then there are face-to-face interviews. If you show genuine interest and drive towards whatever it is you set out to do then more likely than not they will see through the dark spot and consider you.
The past you can do nothing about. The future, yes, and that's where your focus needs to be. If you are struggling with a particular subject, get tutoring; most colleges/universities offer it for free. Internet is also great help; there's a lot of tutoring material available, even whole courses on YouTube. When I took Engineer-In-Training exam a couple of years ago, I hadn't taken some material that was going to be tested, and I learned it watching YouTube videos.
Never settle for low grades. It is hard to get your GPA back up when it starts going down. Assuming you have completed 36 units with 3.48 GPA and need 24 more to graduate (avg AA degree requires 60 units), you will need 27 units with a grade of A in order to attain 3.7 GPA (that is 9 courses 3 units each). Again, not trying to discourage you; just laying out information for you, so it helps you make informed decisions.